Civil Engineering Reference
In-Depth Information
∞
∫
1
8760
V
=
h v dv
⋅ ⋅
(4-24)
mean
0
For c and k values in the range found at most sites, the integral expression
can be approximated to the Gamma function:
)
1
Vc
=+
1
(4-25)
mean
k
For the Rayleigh distribution with k = 2, the Gamma function can be
further approximated to the following:
V
=
090
.
⋅
c
(4-26)
mean
,
which can be used with reasonable accuracy. For example, most sites are
reported in terms of their mean wind speeds. The c parameter in the corre-
sponding Rayleigh distribution is then c = V
This is a very simple relation between the scale parameter c and V
mean
/0.9. The k parameter is of
course 2.0 for the Rayleigh parameters. Thus, we have the Rayleigh distri-
bution of the site using the generally reported mean speed as follows:
mean
2
2
−
v
V
mean
v
c
−
2
v
2
v
()
=
hv
e
=
e
(4-27)
( )
2
2
c
V
mean
4.6.3
Root Mean Cube Speed
The wind power is proportional to the speed cube, and the energy collected
over the year is the integral of h ·
dv. We, therefore, define the “root
mean cube” or the “rmc” speed in the manner similar to the root mean
square (rms) value in the alternating current circuits:
·
v
3
∞
∫
1
8760
3
V
=
h v
⋅ ⋅
dv
(4-28)
3
rmc
0
The rmc speed is useful in quickly estimating the annual energy potential
of the site. Using V
in Equation 4-12 gives the annual average power:
rmc
1
4
3
watts m
2
P
=⋅
ρ
V
(4-29)
rmc
rmc
